We discuss the stability of non-supersymmetric compactifications of M-theory and string theory of the form AdS x X, and their dual non-supersymmetric interacting conformal field theories. We argue that some of the difficulties in controlling 1/N-corrections disappear in the cases that the large N dual conformal field theory has no invariant marginal operators (and in some cases with no exactly marginal operators only). We provide several examples of such compactifications of M-theory down to AdS(4). (C) 1999 Published by Elsevier Science B.V. All rights reserved.